There exists for every inventory
situation a theoretical optimum inventory level. This is the
average inventory needed to provide a given fill rate without the
added problems created by:

Economic order quantity
considerations

Minimum pallet or carton
quantities

Larger than needed purchases
to take advantage of discounts

Other "real-world"
issues that interfere with optimizing inventory turns

This theoretical optimum quantity
is, however, driven by a series of elements that are fundamental
and unique to each and every SKU in the inventory. They are:

The historical pattern of
demand for the item, which in turn determines the
forecast for the item and the mean average deviation
(which is the measurement of the inherent variability of
the item).

The lead time and order
frequency associated with the routine reordering of the
item.

It would be handy to be able to
determine this quantity, either for a given item, or for an
entire group of items. It would provide a base point against
which to measure our actual inventory.

Unfortunately determining the
theoretical optimum inventory (TOI) is not a simple or direct
process. (Least you despair when reading the next few paragraphs,
before we are through we will reduce the problem to a simple
process.)

Determining the TOI is not a
simple function of the forecast or even the reorder target or
reorder point. In fact, you can have two items with the identical
reorder targets and yet have radically different TOIs. This
situation is due to the fact that the relationship of the
lead-time to the order frequency is critical. It so happens that
the reorder target is determined by the sum of the two times
regardless of which is greater. As the inventory replenishment
process takes place, however, the relationship of the two items
has a big influence. Shorter order frequencies play a major roll
in lowering the TOI. For example, you could have two items with
identical forecasts and MADs, one with a lead-time of one
week and an order frequency of every three weeks, and another
item with the reverse. Both will have the same reorder target,
but the one with the one-week order frequency will have a
significantly lower TOI than the other.

The process to determine the TOI
is to plot out the classical "saw tooth" graphs that
result from simulating the reordering process. I provide a series
of examples of this process in my book "A New Era In
Inventory Planning" on page 66. In general the process is
similar to the graph shown in Exhibit A below. The vertical axis
is the amount of inventory that is on hand at any point in time,
and the horizontal axis is the passage of time.

Exhibit A

The interpretation of this saw
tooth graph is that the inventory starts to decease with time as
the product is sold. At some point (determined by the order
frequency) a reorder is triggered (that is the difference between
the reorder target and the net available on hand). Then, after
the lead-time has passed, the product arrives and is put in
stock. The saw tooth rises up to the peak only to start down
again. If you plot these graphs for any variety of items, as I do
in my book on page 66, the process will always come back to the
characteristic saw tooth shown below.

The quantity that is never
penetrated by the saw tooth is the safety stock. In the real
world the safety stock will be penetrated whenever
the demand for the item exceeds the forecast (that is what the
safety stock is for). Conversely, there will be an equal number
of times that the saw tooth does not get down to the safety stock
because the demand was less than the forecast. Consequently on
the average the safety stock will be a layer of inventory
that on the average will always be part of the TOI.

The other part of the TOI is the
average of the height of the saw tooth. In other words, the TOI
will be made up of the safety stock plus half the height of the
saw tooth. This assertion is based on the fact that on the
average half of the saw tooth quantity of stock will be
around at any time. At times there will be the full amount of the
height, and other times it will be right at the bottom, but on
the average it will be half the amount. In our example above the
safety stock is 20 units, and half of the saw tooth is 10 units,
making the TOI 30 for that particular SKU.

By plotting out the TOI for
innumerable SKUs I was able to develop a general
relationship that appears to be universal. It relates the ratio
of the lead-time (LT) of the item over the order frequency (OF),
to the percent of the "base quantity" portion of the
reorder target calculation. (The base quantity is the first part
of the reorder target equation, and is simply the forecast times
the sum of the lead time and order frequency in months.) This
relationship is displayed in Exhibit B.

Exhibit B

Optimum
Inventory

By plotting out the TOI for
innumerable SKUs I was able to develop a general
relationship that appears to be universal. Having developed a
universal formula we were able to have MARS perform the necessary
calculations to come up with the TOI for any group of inventory
items. Before we proceed, however, there are two points worth
noting:

This entire discussion
assumes that the inventories are being routinely
reordered using the methodology of MARS or a comparable
sophisticated reorder target concept. Simplistic systems
or manual estimation of reorders is not going to approach
the efficiencies of the figures being displayed.

Note how the amount of
inventory needed drops when the order frequency is small
(and hence the ratio becomes large). Conversely note how
the amount of inventory needed rises dramatically when
the order frequency is large compare to the lead-time.
This once again, reiterates the point that order
frequency is one of the most important factors in
improving inventory efficiency.

I ran these calculations for a
series of items of various characteristics. The results are
tabulated below:

Item Number

Forecast

Lead Time

Order Freq.

MAD

LT/OF

S.S.

Base

Opt. Inv.

Turns

Test 1

40

14

7

21

2.0

12.3

27.5

17.0

28.3

Test 1a

40

7

14

21

0.5

12.3

27.5

21.4

22.5

Test 2

10

14

14

8

1.0

5.7

9.2

8.0

15.0

Test 2a

10

14

7

8

2.0

4.7

6.9

5.9

20.5

Test 3

500

14

7

52

2.0

30.4

344.3

89.0

67.4

Test 4

4

14

28

5

0.5

4.9

5.5

6.7

7.2

Test 5

1319

30

15

441

2.0

452.3

1946.1

783.2

20.2

Test 6

68

20

30

45

0.7

50.3

111.5

94.9

8.6

Total

1991

Weighted Ave. Turns

31.8

The various examples above offer
some interesting insights to inventory performance. Note the
following:

Items "Test 1 and 1a"
 In these two examples everything is identical except that
the lead time and order frequency are reversed. Note that the
turns are improved by 20% when the order frequency is the lower
figure.

Items test 2 and 2a  In this
case the order frequency is taken down to one week vs. two and
there is a 37% improvement in performance.

Item test 3  This is a fast
moving item with fairly low variability (MAD is only 52 or about
10% of the forecast) and can be ordered weekly. Theoretically you
could see over 60 turns under these ideal conditions!

One key point comes across in the
overall picture. The number of turns is higher than any of us can
even imagine achieving. Remember however, we have not considered
many of the elements that drive inventory levels up such as EOQ,
minimum purchase quantities, discounts, etc. I would estimate
subjectively that these other considerations would in an average
situation cut the turns in half from the TOI levels. Even cut in
half we are looking at very attractive performance levels, and
again, far from what we normally expect to achieve.

These tempered levels are
achievable in my opinion. The elements that prevent us
from hitting these kinds of performance levels are:

Dead stock that has
accumulated and no action is being taken.

Arbitrary overrides by sales
and marketing based on faulty expectations.

Promotion stock-ups that fail
to achieve their sales objectives.

Failure to consistently use
the quantitative system to drive the inventory
replenishments.

MARS-IW allows you to perform the
analysis that I have just outlined in a very simple and efficient
manner. You need only to call up the "Theoretical Optimum
Inventory" feature that in turn brings up the pre-select
screen. This screen gives you the option to select vendors,
locations or all of the company. Upon hitting the calculate
button, the system, in less than a minute, performs all the
calculations and presents the results, both in total, and
subtotaled by vendor and location.